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E39 (1997 - 2003) The BMW 5-Series (E39 chassis) was introduced in the United States as a 1997 model year car and lasted until the 2004 when the E60 chassis was released. The United States saw several variations including the 525i, 528i, 530i and 540i. -- View the E39 Wiki

The (2) on the right are similar to the connectors on the back of the cluster, which which I just became familar. Look closely at the small tab on the curved body where it meets the unlocking device (different color). Press the tab in (the one on the right has three or four ribs which help to identifiy it for this purpose), towards the wiring, and it will allow the unlocking device to pivot or swing over it and at that point it will be obvious. The unlocking device works as a kind of arm that catches some ingenious slotting to lock the thing in place. The one on the left, I have no idea. Bluebee, thanks for all your posts!

If we can figure out how best to remove them, it would make access to the critical fuse F76 much easier, and it would make parasitic drain problems easier to diagnose.
The Bentley diagrams make is look so easy!

You beat me to it. Slide the big black one. There is ribbed end to it and the others you have to use a bit more force. I know it's hard with these cars and plastic pieces that are so damn fragile.

The problem I must have had was that I didn't use enough force (although, trust me, on that big black one, I tugged on the u-shaped clip at left with all the force I had in my fingers, and it only moved a quarter inch - but no more).

On the two levered connectors, I couldn't get the lever over that locking tab.

In both cases, I didn't use tools (for fear of breaking things and making it worse), but I'll try anew with a screwdriver - now that I know force is the answer.

Getting the yellow 40amp FSR fuse F76 out was doable without removing those connectors ... but I'm worried that they must be removed to get the fuse back in.

But, as you surmised, even with little hands, fuse F76 clearly was NOT going to go back in without a fight.

Luckily, removing the big black X254 harness connector to the GM3 module was all that was needed - although - disconnecting THAT connector took more force than I've ever used on ANY plastic connector on the entire bimmer!

LESSON LEARNED:
After having removed & replaced fuse F76, I don't recommend pulling the fuse F75 or F76 unless you absolutely have to. Pull the FSU instead (however, that isn't so easy either).

I just removed the x254 connector to get to F75. The screwdriver tip made it easy. After sliding the connector initially, you will have space at the back end of the connector to push with a screwdriver.

Bluebee, you are a real asset to this board. Thanks for the time you spend posting all the info and links.

can someone confirm that 2002 models have 50amp fuse for aux fan behind glove box?searched in my car and found nothing(will post pics in situ).bentley and others say that aux fan is secured with 50amp fuse.

To gain access to fuses #75 and #76 you don't need to remove all 3 of those big wire bundles on the GM3 module. I had tried to remove and replace fuse #75 as is but this resulted in a lumbosacral strain and abrasions to the dorsal surface of my left had requiring debridement and prophylactic antibiotics. However, you only need to remove the big black wire bundle, not all 3. This will allow sufficient room for a large hand to maneuver a replacement fuse back into place. Here is another tip...always check these fuses first before buying a replacement fan like I did. I had jumped the fan with another batter at its connection and when it did not work I assumed I just needed another fan. Now having read this thread...always use the search funtion first...I tested and replaced the fuse and voila!. The A/C works! Anybody need a used and working OEM replacement fan?

Blue, you are a girl so I assume you have small hands. I was able to remove both fuse #75 and #76 without needing to remove anything, I just slide the passenger seat all the way back, and position myself back on floor and head in the footwell, I can use my fingers remove both fuse and put back, it is tight but small hands helps a lot.